Alex Rodriguez — patron of the arts, beau of female celebrities and modern medical marvel — has the goods to be an all-time baseball villain. Just look at that cocky smile, that still-pretty swing. Read about how many players loathe him.

However, a real villain doesn’t work the media circuit like a second-rate actor plugging a film. He doesn’t prioritize creating noise over wreaking havoc.

He doesn’t turn his adversity into a ridiculous sideshow when, if he means business, he should be taking down The Man.

Or, to borrow from Randy Levine’s return fire yesterday: “It’s time for Alex and his side to put up or shut up.”

The Yankees’ president was responding specifically to one complaint aired by Joseph Tacopina, A-Rod’s newest blustery attorney, to The New York Times. Tacopina accused the Yankees of medical malpractice, alleging the club purposely didn’t inform A-Rod of a serious left hip injury (that eventually required surgery) last October. If this was the case, Levine wondered, then why didn’t A-Rod simply file a grievance through the Players Association?

No matter how much you distrust the authorities, or how loudly you’d revel in A-Rod escaping his current conundrum (just to infuriate the finger-wagging moralists), there’s no getting around Levine’s point.

A-Rod and his clown car full of advisers and lawyers are not behaving like a wronged party. They’re acting like rabble-rousers, trying to create distractions at every turn instead of focusing on the only relevant matter: A-Rod is appealing a 211-game suspension from Major League Baseball for allegedly purchasing and using illegal performance-enhancing drugs on multiple occasions and obstructing MLB’s investigation.

Typically, A-Rod played obtuse last evening, when he met with reporters following the Yankees’ 6-1 loss to the Red Sox at Fenway Park.

“I want to read the Times article,” he said. “I’m going to defer to my lawyer to go about these matters.”

Never mind that we’ve heard these sorts of complaints from Camp A-Rod for months, or that Tacopina’s comments were clearly the kickoff to an orchestrated media campaign, as Page Six reported this past week. Expect Tacopina to hit the television morning talk-show circuit next.

A campaign such as this is precisely contrary to A-Rod’s stated goal last night. As he said: “My goal is to try to lead this team to the postseason. I think we’re in a good place right now. We’re going to continue to work hard and score runs. Winning is still the ultimate goal here.”

If A-Rod needs help in how to be a proper villain, he has a pair of superb role models in the baseball world: His fellow slugger Barry Bonds and his 2007 Yankees teammate Roger Clemens.

Bonds chopped through the thicket of multiple illegal PED allegations, benefited greatly from his former trainer Greg Anderson’s refusal to cooperate with authorities and got stuck only with an obstruction of justice charge that still might be overturned. And he still could get the last laugh on MLB; once his case concludes, the Players Association will decide whether to file a collusion charge from his free agency following the 2007 season.

Clemens, of course, is the king of cojones. MLB expected him to run and hide from its cowardly Mitchell Report, which published allegations about his illegal PED usage without due process. Instead, to the shock of everyone, Clemens proactively went in front of Congress, testified under oath that he didn’t use the stuff and then prevailed in the subsequent perjury hearing. MLB officials are still in denial over what went down there. Clemens could teach Sports Villainy 101.

These are the standards to which A-Rod should aspire. File a grievance against the Yankees for mishandling his health care. Show us the purported video of MLB investigators abusing their extremely limited authority.

We need villains in the entertainment world, but ineffective villains don’t bring anything to the party. They clog our brains and sound waves with nonsense instead of making us think about the way thing are and perhaps should be.

In short, bring it, don’t sing it. Because if he just keeps lobbing verbal grenades, then he’ll live up to one of his many nicknames — A-Fraud — in a whole new way.